i have a dreamcast in my cabinet, as well as a PC. I used a gutted x-arcade for the controls, and they sell an adaptor to connect it to the dreamcast...if you want to use a pc monitor, you can get the dreamcast vga adaptor which works really well.
having a dedicated cabinet for each console would be cool, but not very space efficient..not to mention a pain to make arcade to console controller adaptors. emulation is definatly the way to go. there are some good emulators that run on the dreamcast as well...i know there are nes, snes and genesis emulators that run on the dreamcast....and the best part of using a dreamcast is that it doesnt require any modifications to play homebrew stuff and emulators. just mount it where you can easily access it. mine sits right inside the coin door so i can easily change games. (soul calibur and ikaruga are awesome on the cabinet)
as for emulating the dreamcast, i am not aware of any emulators that work well enough. i have tried a few, but they are usually buggy and slow. i wouldnt reccomend them.(unless you find a good one, in which case i would appreciate being notified)
also, an xbox based system would be good for emulators...if you mod an xbox you can put a big hard drive in it, there are good working emulators for the xbox from everything from the atari 2600 to the playstation. much cheaper than a PC...just a thought.